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"The answer seems to me evident', he declares. Logic has very
little to do with discovery or invention, and memory plays
tricks. Memory however is not so important as it might be. His
own memory, he says without a blush, is bad: 'Why then does
it not desert me in a difficult piece of mathematical reasoning
where most chess players [whose 'memories' he assumes to be
excellent] would be lost? Evidently because it is guided by the
general course of the reasoning. A mathematical proof is not a
mere juxtaposition of syllogisms; it is syllogisms arranged in a
certain order, and the order is more important than the elements
themselves.' If he has the 'intuition' of this order, memory is at
a discount, for each syllogism will take its place automatically
in the sequence.
Mathematical creation, however, does not consist merely in
making new combinations of things already known; 'anyone
could do that, but the combinations thus made would be infinite
in number and most of them entirely devoid of interest. To
create consists precisely in avoiding useless combinations and
in making those which are useful and which constitute only a
small minority. Invention is discernment, selection.' But has
not all this been said thousands of times before? What artist
does not know that selection - an intangible - is one of the
secrets of success? We are exactly where we were before the
investigation began.
To conclude this part of Poincare's observations it may be
pointed out that much of what he says is based on an assump-
tion which may indeed be true but for which there is not a
particle of scientific evidence. To put it bluntly he assumes that
the majority of human beings are mathematical imbeciles.
Granting him this, we need not even then accept his purely
romantic theories. They belong to inspirational literature and
not to science. Passing to something less controversial, we shall
now quote the famous passage in which Poincare describes how
one of his own greatest 'inspirations' came to him. It is meant
to substantiate his theory of mathematical creation. Whether
it does or not may be left to the reader.
He first points out that the technical terms need not be
understood in order to follow his narrative: 'What is of interest